Design Codes: Steel & Footing
Allowable-strength checks for a steel beam in shear and bending with pass/fail utilization gauges, spread-footing sizing against allowable soil pressure, and tolerance stacking — worst case versus statistical RSS. Covers §14.0 and §9.45–9.47.
ASD Shear & Moment: V_a ≤ V_n/Ω_v and M_a ≤ M_n/Ω_b
Utilization: demand over capacity — below 100% passes. FIG. E13-1
Spread Footing: q = P/A ≤ q_allow
Tolerance Stack: Worst Case vs RSS
One dimension per line: nominal ±tolerance, e.g. 25 0.1.
ASD's logic in one line: divide the nominal strength by a safety factor Ω before comparing with the working load. And in tolerance stacking, worst case guards against the impossible-luck assembly while RSS prices in that independent errors rarely all conspire — the difference is often the margin between a manufacturable design and an expensive one.